And which part of the AskTom thread do you think confirms your theory?
Oracle supports Parallel Execution but not in the way you think /
hope.

Oracle can perform parts of the execution plan in parallel by multiple
slave sets but it is based on producer / consumer model having at most
one producer and one consumer active at the same time (within the same
so called "Data Flow Operation" (DFOs) - there can be multiple DFOs
active at the same time but not in such a way as you have in mind).
Hence your idea of two parallel slave sets executing the two branches
below the UNION operator concurrently as producers and feeding the
results into a third consumer is (currently) not supported.

Even with Parallel Execution enabled the rule outlined is still valid:
If the UNION is executed using Parallel Execution, the first child
operation will be executed first in parallel by multiple slaves and as
soon as this is completed, the second child will be started, and so
on.

Remember that the UNION operator (and other operators like FILTER,
UPDATE, DELETE etc.)can have an arbitrary number of child operations,
how many of them would you like Oracle to consider running
concurrently? Therefore Oracle uses a different approach to Parallel
Execution that is independent from such considerations.